So this week I basically beat the Post-Game and caught every non-Shiny Unown. I’m currently repeatedly encountering a low health asleep Entei to try to catch it. I’m using a Wobbuffet to trap it for 2+ turns.

I calculated that you can pretty much fit a full gender in-game living dex into the boxes (420 spaces). Although you don’t quite have space for Deoxys (421st), which can be in your party I suppose.